Problem: Vanessa is 18 years older than Umaima. Twenty years ago, Vanessa was 3 times as old as Umaima. How old is Umaima now?
Answer: We can use the given information to write down two equations that describe the ages of Vanessa and Umaima. Let Vanessa's current age be $v$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $v = u + 18$ Twenty years ago, Vanessa was $v - 20$ years old, and Umaima was $u - 20$ years old. The information in the second sentence can be expressed in the following equation: $v - 20 = 3(u - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $u$ , it might be easiest to use our first equation for $v$ and substitute it into our second equation. Our first equation is: $v = u + 18$ . Substituting this into our second equation, we get the equation: $(u + 18)$ $-$ $20 = 3(u - 20)$ which combines the information about $u$ from both of our original equations. Simplifying both sides of this equation, we get: $u - 2 = 3 u - 60$ Solving for $u$ , we get: $2 u = 58$ $u = 29$.